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When the divisor is greater than 12, and not a composite number, the several quotients must be found by the method of long division, multiplying each remainder by the number of parts which make one of the next lower denomination, and taking in the numbers of the dividend which are of the same denomination, which results are to be successively divided, until all the donominations are gone through, as explained in

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113 - 270 20 - 20 415)2275 z 365)5400 2075 365 200 1750 12 *. 1460 415)2406 - - 290 2075 - - . 12 • 331 - 365)3480 4 - 3285 415)1326 - TT551245 - 4 --• - 81 365)780 - 730

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Cut off two figures from the right hand of the pounds of the dividend; the figures to the left, are the pounds of the quotient ; one-fifth of the figures cut off, are the shillings; to the remainder, if any, annex half the shillings of the dividend, from which, subtract one for every 24 therein, remainder consider as farthings, and those when divided by 4 will give the remainder of the quotient with as much accuracy as is generally required; but for greater, cut off by a perpendicular line the two right-hand figures of the pounds, those to the left will be the pounds of the quotient; multiply the figures cut off by 20, adding in the shillings of the dividend, and set down the two first figures of the product on the right side of the line, and the rest of the product on the left, which will be the shillings; multiply the figures now on the right by 12, adding in the pence of the dividend, and place the product as before, which will give the pence, then multiply the figures now at the right by 4, adding in the farthings of the dividend, and place the product as before; and the several numbers to the left of the line will be the quotient required, and if any number be on the right hand after the last multiplication, it will be the remainder and the numerator of a fraction of a farthing, of which 100 will be the denominator. *

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Let the following be divided in one line, as in simple division

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By the foregoing rules we are enabled to multiply any compound quantity by a mixed number, first multiplying by the integral part of the multiplier, adding thereto the quotient arising from the division of the product of the multiplicand and numerator, by the denominator of the fractional part, or by adding to the first product, such parts of the multiplicand

as the fractional part may be of an unit of the integral part of the multiplier.

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Proof.-Multiply half the mul- Proof.-Multiply one-fourth tiplicand by twice the multi- of the multiplicand, by 4

plier. times the multiplier. 3 0 10 1 19 2 9 23

27, 7 6 - 45 0 10

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